Using vector method, prove that the following points are collinear: A(-3,-2-5),B(1,2,3)and C(3,4,7)

Explanation

We are given the points ` A(-3,-2,-5), quad B(1,2,3) \ and \ C(3,4,7)`


Let the position vectors be :


Position vector of ` A=-3 hat i-2 hat j-5 hat k`


Position vector of ` B= hat i+2 hat j+3 hat k`


Position vector of `C=3 hat i+4 hat j +7 hat k`


Now we have to show that these points are collinear it is possible only if

`|vec(AB)|+|vec(BC)|=|vec(AC)|`


Therefore,


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